Two-step MPS-MFS ghost point method for solving partial differential equations

[1]  C. Fan,et al.  The method of approximate particular solutions for solving certain partial differential equations , 2012 .

[2]  Andreas Karageorghis,et al.  A fictitious points one-step MPS-MFS technique , 2020, Appl. Math. Comput..

[3]  C. S. Chen,et al.  A novel RBF collocation method using fictitious centres , 2020, Appl. Math. Lett..

[4]  C. S. Chen,et al.  The radial basis function differential quadrature method with ghost points , 2020, Math. Comput. Simul..

[5]  B. Fornberg,et al.  A numerical study of some radial basis function based solution methods for elliptic PDEs , 2003 .

[6]  Elisabeth Larsson,et al.  Radial Basis Function Methods for the Rosenau Equation and Other Higher Order PDEs , 2017, Journal of Scientific Computing.

[7]  Liang Yan,et al.  Doubly stochastic radial basis function methods , 2018, J. Comput. Phys..

[8]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[9]  M. Golberg,et al.  Improved multiquadric approximation for partial differential equations , 1996 .

[10]  Bengt Fornberg,et al.  A Pseudospectral Fictitious Point Method for High Order Initial-Boundary Value Problems , 2006, SIAM J. Sci. Comput..

[11]  Ching-Shyang Chen,et al.  A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆ 2 ± λ 2 , 2009 .

[12]  C. S. Chen,et al.  Particular solutions of Helmholtz-type operators using higher order polyhrmonic splines , 1999 .

[13]  C. S. Chen,et al.  Kansa-RBF Algorithms for Elliptic Problems in Axisymmetric Domains , 2016, SIAM J. Sci. Comput..

[14]  Song Xiang,et al.  Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation , 2012 .

[15]  Graeme Fairweather,et al.  The method of fundamental solutions for the numerical solution of the biharmonic equation , 1987 .

[16]  E. Kansa,et al.  Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations , 2000 .

[17]  Shmuel Rippa,et al.  An algorithm for selecting a good value for the parameter c in radial basis function interpolation , 1999, Adv. Comput. Math..

[18]  Graeme Fairweather,et al.  The method of fundamental solutions for elliptic boundary value problems , 1998, Adv. Comput. Math..

[19]  Scott A. Sarra,et al.  A random variable shape parameter strategy for radial basis function approximation methods , 2009 .

[20]  Andreas Karageorghis,et al.  Improved Kansa RBF method for the solution of nonlinear boundary value problems , 2018 .